IT’S hard to imagine a movie much more exciting than “The Bourne Ultimatum,” which is not only far and away this summer’s best three-peat, it’s a pulse-pounding peak to Matt Damon’s spy trilogy. Director Paul Greengrass – who directed the superb “United 93″ between the second and third “Bourne” installments – knows how to stage and edit bravura action sequences, generating almost unbearable suspense while deploying a superb cast.

At the center of “Ultimatum” is Damon’s finely shaded performance as the enigmatic CIA killing machine known as Jason Bourne, who continues his quest to discover his true identity – and wreak vengeance on the spooks who took it and his girlfriend away from him.

After eluding pursuers in Moscow, rogue agent Jason pops up in London, where a reporter for the Guardian (Paddy Considine) has been writing about Jason and Blackbriar, the CIA black-ops program that replaced the one that produced Jason.

Noah Vosen (David Strathairn of “Good Night, and Good Luck,” effectively cast against type), who heads the program, is determined to cover his tracks by ordering the assassination of Bourne and anyone in a position to help him.

An astounding chase sequence in London’s very crowded Waterloo station is intercut with scenes of Vosen in New York, who directs Bourne’s pursuers using London’s “Ring of Steel”

surveillance-camera system.

This chase is followed by an even neater one through the narrow alleys and over the roofs of Tangier – where Bourne finally engages in visceral hand-to-hand combat with a killer in a tiny bathroom.

One great thing about this smartly developed series is that Bourne doesn’t use high-tech gadgets – he works with his wits and whatever’s available. In Bourne’s experienced hands, a toothbrush or a washcloth can become a deadly weapon.

Bourne’s globetrotting trail leads to New York, where Vosen’s extra-legal tactics are being questioned by high-ranking CIA investigator Pamela Landy (Joan Allen). But does she having the backing of the agency’s director (Scott Glenn)?

The tension ratchets up as Vosen and Bourne play a cat-and-mouse game in the Big Apple, where the classic chase in “The French Connection” is arguably topped by a breathtaking vehicular pursuit beginning at the Port Authority Bus Terminal.

It all ends on the Upper East Side, where Bourne confronts the Mengele-like doctor (a short but highly effective appearance by Albert Finney) who used torture and other methods to turn Bourne into an identity- and conscience-free killer.

The screenplay by Tony Gilroy (who wrote the first two Bourne flicks), Scott Z. Burns and George Nolfi, very loosely adapted from Robert Ludlum’s Cold War-era novel, repeatedly raises – but doesn’t dwell – on the issue of how far intelligence agencies should go to protect us in the 9/11 era.

But as in the two previous Bournes, it grounds the film in a 21st-century reality that’s generally missing from the genre – even as Damon’s unflashy spook harks back to the low-key, morally ambiguous spies played by Michael Caine in the 1960s and 1970s.

The story does strain credulity repeatedly, especially when Bourne just happens to re-encounter former CIA colleague Nicky Parsons (Julia Stiles, in her most substantial “Bourne” appearance to date).

And how exactly does Bourne emerge from a grisly car wreck on South Street without a scratch?

“The Bourne Ultimatum” moves with such assurance, and at such a lightning pace, to effectively render such questions moot. Once again, the Bourne-again spy makes James Bond, Ethan Hunt and their quaint adventures seem like something of the last century.